Riggifying. How to make the arms and fingers bend with the armature?
It's hard to tell without the file.
here couple of points to consider:
Activate normalize in options
go through the vertex groups to verify that unrelated bones don't influence the given region. Ex. fingers on the upper arm.
If yes, then subtract it.
In case you didn't try watching - enter link description here
DanPro tutorials are brilliant and provide useful tips.
Remember also that the hand is a very complex mechanism, not only 3D, real hands are not intuitive organs, it's one of hardest parts of rigging.